All Algebra II Resources
Example Question #1 : Geometric Sequences
Which of the following is a geometric sequence?
A geometric sequence is one in which the next term is found by mutlplying the previous term by a particular constant. Thus, we look for an implicit definition which involves multiplication of the previous term. The only possibility is:
Example Question #2 : Geometric Sequences
What is the explicit formula for the above sequence? What is the 20th value?
This is a geometric series. The explicit formula for any geometric series is:
, where is the common ratio and is the number of terms.
In this instance and .
Substitute into the equation to find the 20th term:
Example Question #3 : Geometric Sequences
What type of sequence is shown below?
None of the other answers
None of the other answers
This series is neither geometric nor arithmetic.
A geometric sequences is multiplied by a common ratio () each term. An arithmetic series adds the same additional amount () to each term. This series does neither.
Mutiplicative and subtractive are not types of sequences.
Therefore, the answer is none of the other answers.
Example Question #4 : Geometric Sequences
Identify the 10th term in the series:
The explicit formula for a geometric series is
In this problem
Example Question #5 : Geometric Sequences
Which of the following could be the formula for a geometric sequence?
The explicit formula for a geometric series is .
Therefore, is the only answer that works.
Example Question #6 : Geometric Sequences
Find the 15th term of the following series:
This series is geometric. The explicit formula for any geometric series is:
Where represents the term, is the first term, and is the common ratio.
In this series .
Therefore the formula to find the 15th term is:
Example Question #7 : Geometric Sequences
Example Question #8 : Geometric Sequences
Find the sum for the first 25 terms in the series
Before we add together the first 25 terms, we need to determine the structure of the series. We know the first term is 60. We can find the common ratio r by dividing the second term by the first:
We can use the formula where A is the first term.
The terms we are adding together are so we can plug in :
Common mistakes would involve order of opperations - make sure you do exponents first, then subtract, then multiply/divide based on what is grouped together.
Example Question #9 : Geometric Sequences
Give the 33rd term of the Geometric Series
[2 is the first term]
First we need to find the common ratio by dividing the second term by the first:
The term is
so the 33rd term will be
Example Question #10 : Geometric Sequences
Find the 19th term of the sequence
[the first term is 7,000]
First find the common ratio by dividing the second term by the first:
Since the first term is , the nth term can be found using the formula
so the 19th term is